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GATE 2025 PH – Question 37

Electromagnetic theory · multipole expansion · 2 marks · Multiple choice

The wire loop shown in the figure carries a steady current I. Each straight section of the loop has length d. A part of the loop lies in xy plane and the other part is tilted at 30° with respect to the xz plane. The magnitude of the magnetic dipole moment of the loop (in appropriate units) is

Six-segment bent current loop, partly in the xy plane and partly tilted 30 degrees from the xz plane.
  1. $\sqrt2Id^2$
  2. $2Id^2$
  3. $\sqrt3Id^2$
  4. $Id^2$

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Correct answer: (C) $\sqrt3Id^2$

Explanation

The loop is the boundary of two squares of area $d^2$. Their oriented area vectors have angle 60 degrees, so $|\boldsymbol\mu|=Id^2\sqrt{2+2\cos60^\circ}=\sqrt3Id^2$.